Hello and welcome to the forum!
No, anxiety and stress will not cause TB, however, your recent epsiode of TB and the worry of it returning WILL cause anxiety.
You need to keep following up with your doctor. People who have had active TB are at a significantly increased risk of developing it again. If you have TB-like symptoms again and are worried, you can ask your doctor to do more definitive testing to rule it out. In addition to a chest xray, he could do a blood test and a sputum (coughed up mucous) test for TB. If he still says you're in the clear, you may have to accept that perhaps the asthma symptoms are causing you a great deal of anxiety and address it.
It's quite unfortunate that you would get a diagnosis of a condition whose symptoms mimic that of TB, but you have to rely on what your doctor is telling you. Going through TB is stressful enough, physically and mentally...but then you have a reemergence of similar symptoms. Anyone would have been frightened.
Take good care of yourself and keep working with your doctor. If your anxiety isn't improving, start addressing it with a professional. And, while anxiety and stress certainly is NOT good for our overall wellbeing, it isn't going to cause an infectious disease like TB.